Related papers: Properties of Carry Value Transformation
In this paper, we reveal the importance and benefits of introducing second-order operations into deep neural networks. We propose a novel approach named Second-Order Response Transform (SORT), which appends element-wise product transform to…
Very recently we have witnessed a new development of quantum information, the so-called continuous variable (CV) quantum information theory. Such a further development has been mainly due to the experimental and theoretical advantages…
We prove in this paper that the weighted volume of the set of integral transportation matrices between two integral histograms r and c of equal sum is a positive definite kernel of r and c when the set of considered weights forms a positive…
The Burrows-Wheeler Transform (BWT) is an efficient invertible text transformation algorithm with the properties of tending to group identical characters together in a run, and enabling search of the text. This transformation has extensive…
The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…
Determining the number of factors is essential to factor analysis. In this paper, we propose {an efficient cross validation (CV)} method to determine the number of factors in approximate factor models. The method applies CV twice, first…
A conflict-free replicated data type (CRDT) is an abstract data type, with a well defined interface, designed to be replicated at multiple processes and exhibiting the following properties: (1) any replica can be modified without…
Clustering is the task of gathering similar data samples into clusters without using any predefined labels. It has been widely studied in machine learning literature, and recent advancements in deep learning have revived interest in this…
In theory, vector quantization (VQ) is always better than scalar quantization (SQ) in terms of rate-distortion (R-D) performance. Recent state-of-the-art methods for neural image compression are mainly based on nonlinear transform coding…
In order to deal with variant-length long videos, prior works extract multi-modal features and fuse them to predict students' engagement intensity. In this paper, we present a new end-to-end method Class Attention in Video Transformer…
Continuous variable (CV) quantum computation offers an alternative to qubit-based computing by exploiting the infinite-dimensional Hilbert space of bosonic modes. Despite recent progress, superconducting platforms have yet to demonstrate a…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Near-lossless image compression-decompression scheme is proposed in this paper using Zipper Transformation (ZT) and inverse zipper transformation (iZT). The proposed ZT exploits the conjugate symmetry property of Discrete Fourier…
The contributions of this paper are twofold. First, we show the potential interest of Complex-Valued Neural Network (CVNN) on classification tasks for complex-valued datasets. To highlight this assertion, we investigate an example of…
Conditional Value-at-Risk (CoVaR) quantifies systemic financial risk by measuring the loss quantile of one asset, conditional on another asset experiencing distress. We develop a Transformer-based methodology that integrates financial news…
For computer vision, Vision Transformers (ViTs) have become one of the go-to deep net architectures. Despite being inspired by Convolutional Neural Networks (CNNs), ViTs' output remains sensitive to small spatial shifts in the input, i.e.,…
Piecewise Translations is a class of dynamical systems which arises from some applications in computer science, machine learning, and electrical engineering. In dimension 1 it can also be viewed as a non-invertible generalization of…
A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of…
Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size…